1. Given the polynomial f(x) = 0.0074x4 - 0.284x3 + 3.355x2 - 12.183x + 5. Applying Newton - Raphson to find a real roo

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1. Given the polynomial f(x) = 0.0074x4 -
0.284x3 + 3.355x2 - 12.183x + 5.
Applying Newton - Raphson to find a real root that exist between 15
and 20 (initial guess; 16.15).
2. Given the integral (6
+ 3cosx)dx
i. Solve using Trapezoidal rule (single application)
ii. Solve using Analytical method
iii. Solve using Composite Trapezoidal rule, when n = 3, n=
4.
iv. Solve using Simpson's rule (single application)
v. Solve using Composite Simpson 1/3 rule. When n = 4.
3. Given the following expression
Xe2x dx
f(x) = xe2x , given n = 5, use composite Simpson to
solve for the integral.